Hot Jupiters with Relatives: Discovery of Additional Planets in Orbit Around WASP-41 and WASP-47?,??

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A&A 586, A93 (2016) Astronomy DOI: 10.1051/0004-6361/201526965 & c ESO 2016 Astrophysics

Hot Jupiters with relatives: discovery of additional planets in orbit around WASP-41 and WASP-47?,??

M. Neveu-VanMalle1,2, D. Queloz2,1, D. R. Anderson3, D. J. A. Brown4, A. Collier Cameron5, L. Delrez6, R. F. Díaz1, M. Gillon6, C. Hellier3, E. Jehin6, T. Lister7, F. Pepe1, P. Rojo8, D. Ségransan1, A. H. M. J. Triaud9,10,1, O. D. Turner3, and S. Udry1

1 Observatoire Astronomique de l’Université de Genève, Chemin des Maillettes 51, 1290 Sauverny, Switzerland e-mail: [email protected] 2 Cavendish Laboratory, J J Thomson Avenue, Cambridge, CB3 0HE, UK 3 Astrophysics Group, Keele University, Staﬀordshire, ST5 5BG, UK 4 Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK 5 SUPA, School of Physics and Astronomy, University of St. Andrews, North Haugh, Fife, KY16 9SS, UK 6 Institut d’Astrophysique et de Géophysique, Université de Liège, Allée du 6 Août, 17, Bat. B5C, 19C 4000 Liège 1, Belgium 7 Las Cumbres Observatory Global Telescope Network, 6740 Cortona Dr. Suite 102, Goleta, CA 93117, USA 8 Departamento de Astronomía, Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile 9 Centre for Planetary Sciences, University of Toronto at Scarborough, 1265 Military Trail, Toronto, ON, M1C 1A4, Canada 10 Department of Astronomy & Astrophysics, University of Toronto, Toronto, ON, M5S 3H4, Canada

Received 14 July 2015 / Accepted 30 September 2015

ABSTRACT

We report the discovery of two additional planetary companions to WASP-41 and WASP-47. WASP-41 c is a planet of minimum mass 3.18 ± 0.20 MJup and eccentricity 0.29 ± 0.02, and it orbits in 421 ± 2 days. WASP-47 c is a planet of minimum mass 1.24 ± 0.22 MJup and eccentricity 0.13 ± 0.10, and it orbits in 572 ± 7 days. Unlike most of the planetary systems that include a hot Jupiter, these two systems with a hot Jupiter have a long-period planet located at only ∼1 au from their host star. WASP-41 is a rather young star known to be chromospherically active. To differentiate its magnetic cycle from the radial velocity effect induced by the second planet, we used the emission in the Hα line and find this indicator well suited to detecting the stellar activity pattern and the magnetic cycle. The analysis of the Rossiter-McLaughlin effect induced by WASP-41 b suggests that the planet could be misaligned, though an aligned orbit cannot be excluded. WASP-47 has recently been found to host two additional transiting super Earths. With such an unprecedented architecture, the WASP-47 system will be very important for understanding planetary migration. Key words. stars: individual: WASP-47 – stars: individual: WASP-41 – techniques: photometric – techniques: radial velocities – techniques: spectroscopic – planetary systems

1. Introduction between 0.8 and 5 au (Curiel et al. 2011). Ten years later, the discovery of the planetary system around HIP 14810 (Wright et al. In contrast to the large number of multiple planetary systems, 2007, 2009) revealed that a hot Jupiter can be found in a system stars with hot-Jupiter planets have long been thought to lack ad- with smaller planets on wider orbits. From 15 years of radial ve- ditional planets. Recent studies suggest that this statement may locity surveys, Feng et al.(2015) recently constrained the orbits not be true (e.g. Knutson et al. 2014). However the existence of of the distant (P > 9 years) giant planets in orbit around the hot- those additional planets was revealed by nothing more than ra- Jupiter hosts HD 187123 and HD 217107. Among all systems dial velocity trends. Only seven outer planetary companions of with a close-in giant planet discovered by transit surveys, only close-in (a < 0.1 au) giant planets have a full orbital period that HAT-P-13 (Bakos et al. 2009), HAT-P-46 (Hartman et al. 2014), has been observed. and Kepler-424 (Endl et al. 2014) have an additional planetary The multiple planetary system around υ Andromedae (Butler companion detected by Doppler surveys with a fully measured et al. 1997) was the ﬁrst to be found with a hot Jupiter. This orbit. planet is surrounded by three more massive giant planets orbiting The Wide Angle Search for Planets (WASP, Pollacco et al. ? Using data collected at ESO’s La Silla Observatory, Chile: HARPS 2006) has discovered more than 100 hot Jupiters. While some on the ESO 3.6 m (Prog ID 087.C-0649 & 089.C-0151), the Swiss of them clearly have a very distant companion (e.g. WASP-8, Euler Telescope, TRAPPIST, the 1.54-m Danish telescope (Prog Queloz et al. 2010), none of them were previously known to have CN2013A-159), and at the LCOGT’s Faulkes Telescope South. a fully resolved orbit. ?? Photometric lightcurve and RV tables are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) The radial velocity follow-up observations of WASP initi- or via ated in 2008 with the ﬁbre-fed echelle spectrograph CORALIE http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/586/A93 (mounted on the 1.2-m Euler Swiss telescope at La Silla) has

Article published by EDP Sciences A93, page 1 of 12 A&A 586, A93 . (2016) . identified new multiple systems including a hot Jupiter. We re- 0.6 port here the detection of additional planets around WASP-41 (Maxted et al. 2011) and WASP-47 (Hellier et al. 2012). These 0.5 new planets are both located only ∼1 au of their parent star. 0.4 When searching for long-period companions using the radial ve- 0.3 locities technique, the effects of stellar activity should be care- 0.2 Normalised power fully considered to avoid misdetections. A stellar magnetic cycle Normalized power 0.1 may mimic the signal of a planetary companion (e.g. Lovis et al. 0.0 2011). WASP-41 is known to be active (Maxted et al. 2011), 2.5.10.0 20. 50. 100.0 200. 500. 1000. which makes it important to recognise the temporal structure of . Period [days] . its magnetic cycle. Since the photospheric Ca (H & K) emission lines cannot be extracted from single CORALIE spectra (insuffi- Fig. 1. WASP-47 Lomb-Scargle periodogram of the residuals after sub- cient signal-to-noise ratio), we alternatively use the emission in tracting Planet b. The dotted lines correspond to a false-alarm probabil- the Hα band to characterise activity. We find that this indicator ity of 0.1%, 1%, and 10%. is very well suited to WASP-41, though it may not be true in general (Cincunegui et al. 2007). Monte-Carlo (MCMC) fitting scheme to derive the system pa- Section2 reports the observations, analysis, and results for rameters of the two-planet model. We did not include the WASP WASP-47. Section3 similarly addresses the case of WASP-41 photometry in our analysis because it has poor precision com- with a description of the various additional observations, a study pared to EulerCAM and might suffer from spatial dilution from of the stellar activity, and an analysis that includes the Rossiter- background stars. We used the most recent version of the code McLaughlin effect followed by the results. In Sect.4, after dis- described in Gillon et al.(2012) and references therein. The cussing the importance of considering magnetic cycles when jump parameters used in our analysis to characterise the tran- searching for long-period planets, we compare our two multi- siting planet WASP-47b were ple planetary systems, including a hot Jupiter, to the five previously known ones. We discuss the biases induced by the observ- – the transit depth defined as the planet/star area ratio (dF = 2 ing strategies of Doppler and transit surveys in finding multiple (Rp/R?) ), where Rp and R? are the planetary and stellar ra- planetary systems including a hot Jupiter. Finally we check the dius, respectively; transit probabilities of WASP-47c and WASP-41c. – the transit impact parameter in the case of a circular orbit 0 During the process of revision of this paper, Becker et al. (b = ab cos ip,b/R?), where ab and ip,b are the semi-major (2015) reported the presence of two additional super-Earths tran- axis and the inclination of the planetary orbit, respectively; siting WASP-47 every ∼0.8 and 9 days. This remarkable discov- – the transit duration T14, from first to last contact; ery brings strong constraints on the migration of this system and – the orbital period Pb; will be discussed in the last section. – the time of inferior conjunction√ T0,b; √ – the two parameters eb cos ωb and eb sin ωb, where eb is the eccentricity and ωb the argument of periastron; 2. WASP-47 c q − 2 1/3 – the parameter K2,b = Kb 1 eb Pb , where Kb is the radial 2.1. Observations velocity semi-amplitude. WASP-47 is a G9V star hosting a giant planet with a mass of For the period Pb and time of inferior conjunction T0,b, we im- 1.14 MJup and a period of 4.16 days (Hellier et al. 2012). The posed Gaussian priors defined by the values derived in Hellier discovery paper includes 19 radial velocity measurements taken et al.(2012), since we did not include the WASP photometry in with CORALIE during two observing seasons. Ongoing moni- our analysis. Uniform priors were assumed for the probability toring revealed a possible third body, and after 46 observations distribution functions (PDFs) of all the other jump parameters. over 4.44 years, the orbit of a second planet was clear. After The choices of jump parameters were optimised to reduce the subtracting the inner planet (hot Jupiter) from the radial velocity dependencies between the parameters√ and thus to minimise√ the data, the analysis of the residuals using a Lomb-Scargle peri- correlations. We checked that using e cos ω and e sin ω as odogram shows a clear peak around 550 days (see Fig.1). The jump parameters translates into a uniform prior on e and does analysis of the residuals after subtracting the two-planet model not influence the results. shows no additional signal (see Fig. A.1). We modelled the limb-darkening with a quadratic law, where In November 2014, an upgrade of CORALIE was per- instead of the coefficients u1 and u2, we used the combinations formed. The changes introduced an offset in the radial velocities. c1 = 2×u1 +u2 and c2 = u1 −2×u2 as jump parameters in order to Since the orbit of the outer planet was not fully covered in phase, minimise the correlation of the obtained uncertainties (Holman we collected six additional measurements from June to August et al. 2006). We assumed normal priors on u1 and u2 with the 2015. One measurement was done right after the upgrade just values deduced from the tables by Claret & Bloemen(2011). As before the star became unobservable but it suffered from day- described in Gillon et al.(2012), we applied a correction factor light contamination and had to be discarded. For the analysis, CF = 1.32 to the error bars of the photometric data to account the 2015 data are considered as an independent radial velocity for the red noise. data set. WASP-47 c does not have transit observations, the jump parameters used in our analysis to define the second orbit were 2.2. Analysis – the orbital period Pc; We combined the photometry data from EulerCAM (Gunn-r0 – the time of inferior conjunction√ T0,c;√ filter) published in Hellier et al.(2012) with all the radial ve- – the two parameters ec cos ωc and ec sin ωc; p 2 1/3 locities from CORALIE and used an adaptive Markov chain – the parameter K2,c = Kc 1 − ec Pc .

A93, page 2 of 12 M. Neveu-VanMalle et al.: Hot Jupiters with relatives

We assumed uniform priors on all those jump parameters. Table 1. Median and 1σ limits of the posterior marginalised PDFs The stellar density is derived at each step of the MCMC from obtained for the WASP-47 system derived from our global MCMC Kepler’s third law and the values of the scale parameter ab/R? analysis. and orbital period of WASP-47b (Winn et al. 2010). The stellar mass M? is obtained thanks to a calibration (Enoch et al. MCMC Jump parameters 2010; Gillon et al. 2011) from well-constrained binary systems Star (Southworth 2011). This empiric law is a function of Teff, ρ? Teff [K] 5576 ± 68 and [Fe/H]. We used Gaussian prior distributions for Teff and [Fe/H] 0.36 ± 0.05 ± [Fe/H], and the initial value for ρ?, based on the values derived c1 1.17 0.03 by Mortier et al.(2013). c2 −0.02± 0.02 Planet b Pb [d] 4.1591409 ± 0.0000072 2.3. Results T√0,b – 2 450 000 [BJDTDB] 5764.3463 ± 0.0002 √eb cos ωb 0.04 ± 0.06 The results presented in Table1 have been obtained running e sin ω 0.01 ± 0.09 b qb five chains of 100 000 accepted steps. The derived values are K = K 1 − e2 P1/3 [m s−1 d1/3] 225.7 ± 3.6 the median and 1σ limits of the marginalised posterior distribu- 2,b b b b Planet c tions, considering a 20% burn-in phase. The acceptance fraction Pc [d] 572 ± 7 is ∼25% (∼40% for the burn-in phase). We used the statistical T – 2 450 000 [BJD ] 5981 ± 16 test of Gelman & Rubin(1992) to check the convergence of the √0,c TDB √ec cos ωc −0.21 ± 0.24 chains and get a potential scale reduction factor (PSRF) smaller ec sin ωc 0.16 ± 0.20 than 1.01 for all the jump parameters. The autocorrelations are p 2 1/3 −1 1/3 K2,c = Kc 1 − ec Pc [m s d ] 248 ± 43 shorter than 2000 steps except for the semi-amplitude and the Derived parameters eccentricity of the outer planet. The lack of data around the ra- Star dial velocity minimum introduces a small degeneracy between u 0.462 ± 0.014 these parameters. Their autocorrelations are ∼5000 steps long. 1 u2 0.242 ± 0.010 As we did not include additional transit light curves, we did not Density ρ? [ρ ] 0.68 ± 0.06 improve the determination of the transit parameters compared to Surface gravity log g? [cgs] 4.32 ± 0.05 Hellier et al.(2012). They are not given here for this reason. The Mass M? [M ] 1.026 ± 0.076 best fit solution for the radial velocities is plotted in Fig.2. The Radius R? [R ] 1.15 ± 0.04 values provided in Table1 are the median values of the posterior Luminosity L? [L ] 1.14 ± 0.11 distributions and not the best fit values used in Fig.2. To verify Planet b that the median values represent a self-consistent set of parame- Mass Mp,b [MJup] 1.13 ± 0.06 −1 ± ters, we compare the BIC (Bayesian Information Criterion) ob- RV amplitude Kb [m s ] 140 2 Orbital eccentricity eb <0.026 (at 2σ) tained using the median values and the best fit values. We obtain Orbital semi-major axis a [au] 0.051 ± 0.001 compatible results. b Density ρp,b [ρJ] 0.71 ± 0.08 Including the data collected in 2015 allows to reduce the un- Surface gravity log gp,b [cgs] 3.33 ± 0.03 ∗ certainty on the eccentricity and semi-amplitude of the outer Equilibrium temperature Teq,b [K] 1275 ± 23 planet. All the other parameters remain unchanged compared Planet c to the results obtained with the first data set alone. The poste- Minimum mass Mp,c sin ip,c [MJup] 1.24 ± 0.22 −1 rior distribution of the offset between the two data sets (∆RV = RV amplitude Kc [m s ] 30 ± 6 − ± 1 Orbital eccentricity ec 0.13 ± 0.10 18 11 m s ) agrees with what has been observed on bright ◦ radial velocity standards. Argument of periastron ωc [ ] 144 ± 53 The semi-amplitude of WASP-47 c is barely twice as large Orbital semi-major axis ac [au] 1.36 ± 0.04 Equilibrium temperature T (∗) [K] 247 ± 5 as the radial velocity uncertainties, and the phase coverage is eq,b incomplete. To validate the detection, we compared the results ac/R? 255 ± 7 obtained when running the same MCMC with a model includ- Notes. (∗) Assuming zero albedo and efficient redistribution of energy. ing only one planet. With the one-planet model, the reduced χ2 on the initial set of radial velocities is 2.7 and the residual root mean square (rms) 19.2 m s−1. When fitting two planets, the corresponding reduced χ2 is 1.2 and the residual rms 10.6 m s−1. of ∼100 m s−1 and triggered an intensive monitoring of the tar- The two-planet model is clearly preferable. get. An additional planet on an eccentric orbit rapidly became apparent. Because of the significant eccentricity of the second planet combined with a period close to one year, we had to wait 3. WASP-41 c until the fifth year of follow-up to plan observations at the peri- 3.1. Observations astron with a good sampling. After subtracting the inner planet (hot Jupiter) from the radial velocity data, the analysis of the WASP-41 is a G8V star hosting a giant planet with a mass of residuals using a Lomb-Scargle periodogram shows a clear peak 0.9 MJup and a period of 3.05 days (Maxted et al. 2011). The around 400 days (see Fig.3). The additional peaks present at discovery paper includes 22 radial velocity measurements taken ∼200 days and ∼130 days correspond to the two first harmon- within four months (excluding the first point). The short time ics P/2 and P/3. Such features are expected when applying fre- span of the observations did not allow for detecting any addi- quency decomposition to eccentric signals, and WASP-41c has tional signal. We did a follow-up on the star and collected a an eccentricity e ∼ 0.3. The analysis of the residuals, after sub- total of 100 radial velocities with CORALIE over 4.46 years. tracting the two planets from the radial velocities, shows no ad- The observations during the second season revealed an offset ditional periodic signal (see Fig. A.2).

A93, page 3 of 12 A&A 586, A93 (2016)

150 Table 2. Additional transit observations of WASP-41b and applied cor-

] 100 Pb =4.16 d 1 rection factors. − 50 s 0 m [ 50 Instrument Filter Date CF V

R 100 FTS PanSTARRS z 12 Apr. 2011 1.8 150 21 Mar. 2011 1.0 0.4 0.2 0.0 0.2 0.4 02 Apr. 2011 2.1 60 TRAPPIST I + z 12 May 2011 2.0

] 40 Pc =572 d 09 Mar. 2012 1.5 1

− 20 s 19 Apr. 2013 1.4 0 m 19 Apr. 2013 2.2 [ 20 Danish R ∗ V 25 Apr. 2013 3.0

R 40 60 (∗) 0.4 0.2 0.0 0.2 0.4 Notes. Partial transit. Φ Fig. 2. WASP-47 CORALIE radial velocity data (blue/green dots: be- The emission in the Hα line is a rather underused activity fore/after the upgrade) and best ﬁt model (red line). Top: phase-folded indicator to trace photospheric stellar activity. In their study, on the period of the inner planet (outer planet subtracted). Bottom: Cincunegui et al.(2007) concluded that the activity measured phase-folded on the period of the outer planet (inner planet subtracted). 0 . . in the Hα was not equivalent to the RHK indicator. They did not measure similar correlations between the two indicators in their whole sample. Some of their stars showed correlations, when 0.8 others showed no or anti-correlations. Using solar observations,

0.6 Meunier & Delfosse(2009) demonstrated that the Ca II (H & K) and the Hα emissions have different behaviours. During an 0.4 active period when the filaments reach saturation, they observe a positive correlation between the indicators. On the other hand, 0.2 Normalised power Normalized power during moderate active periods, the filaments counteract the ef- 0.0 fect of plages on the Hα measurements, leading to weak or neg- 2.5.10.0 20. 50. 100.0 200. 500. 1000. ative correlations. Gomes da Silva et al.(2014) conclude that 0 . Period [days] . active stars with a mean log RHK ≥ −4.7 systematically show a positive correlation between the Ca II (H & K) and Hα flux. Fig. 3. WASP-41 Lomb-Scargle periodogram of the residuals after sub- 0 Since WASP-41 is a very active star with log RHK ≥ −4.7, it tracting Planet b. The dotted lines correspond to false-alarm probabili- is reasonable to use Hα as an activity indicator. The motivation ties of 0.1%, 1%, and 10%. to use this band is that it is located in the red part of the stellar spectrum where a high signal-to-noise ratio can be obtained from We used the HARPS spectrograph mounted on the 3.6-m the CORALIE spectra. As suggested in Cincunegui et al.(2007), telescope in La Silla to observe the Rossiter-McLaughlin effect we measured the Hα emission at 6562.808 Å and the continuum induced by WASP-41 b during the transit on 3 Apr. 2011. In centred at 6605 Å and averaged on a window 20 Å wide. Unlike addition to the Rossiter-McLaughlin observations, 30 measure- Cincunegui et al.(2007) we extracted the H α from a 0.6 Å wide ments out of transit of WASP-41 were gathered with HARPS band instead of 1.5 Å. between Apr. 2011 and Aug. 2012 to confirm the second signal The Hα index reveals a time variation similar to the one ob- detected with CORALIE. served on the FWHM (Fig.4) that can be modelled by a third- More transit light curves of WASP-41 b have been obtained order trend in time. It is then reasonable to conclude that we are since the publication of the discovery paper: with the Faulkes observing the magnetic cycle of WASP-41. After subtracting the Telescope South (FTS) at Siding Spring Observatory and with third-order trend, we analysed the Lomb-Scargle periodogram the TRAPPIST telescope (Jehin et al. 2011) and the Danish tele- of the residuals in the FWHM. A clear peak appears at exactly scope both in La Silla. Details of these observations can be found one year (see Fig.5). The same one-year signal in the FWHM in Table2. has been observed on the brighter stars also regularly observed with CORALIE, as well as with similar instruments (SOPHIE, 3.2. Study of stellar activity HARPS). When we look at the Lomb-Scargle periodogram of the Hα index after subtracting the long-term trend, a peak ap- WASP-41 is known to be an active star (Maxted et al. 2011). pears at ∼18 days (see Fig.6). Interestingly, this corresponds to In spite of the large amplitude of the second signal, we check the rotation period of the star derived from the WASP photome- that it is not due to a stellar magnetic cycle. For that purpose try by Maxted et al.(2011). we searched for correlations between the radial velocities and Encouraged by the interesting result obtained using the spectral activity indicators. No variation is observed in the bi- Hα index on WASP-41, we looked at the similarly active star 0 sector span of the cross correlation function (Fig. A.2 bottom CoRoT-7 (with log RHK = −4.62 ≥ −4.7). Queloz et al.(2009) panel). The full width at half maximum (FWHM) shows some note that CoRoT-7 shows strong variability in the FWHM, com- variability, which is suspiciously similar to the radial velocities’ parable to what is observed on WASP-41. CoRoT-7 benefitted 0 variability (periodicity close to 400 days). The log RHK extracted from simultaneous photometric and spectroscopic observations from the HARPS spectra, based on the photospheric Ca II (H & (see Haywood et al. 2014). We extracted the Hα index from the K) lines, indicates a mean value of −4.483 ± 0.036 characteristic HARPS spectra of CoRoT-7 in the same way as WASP-41. A 0 of an active star. But no variation in the log RHK is visible during very clear correlation is observed between the Hα index and the the two years of HARPS data (Fig. A.3). FWHM (see Fig.7). After subtracting a third-order trend, very

A93, page 4 of 12 M. Neveu-VanMalle et al.: Hot Jupiters with relatives ]

1 0.15 0.03 −

s 0.10

m 0.05 k

[ 0.02 0.00

M 0.05 H 0.10 W x F 0.01 0.15 e ∆ d n i

α 0.00 0.04 H x ∆

e 0.02 d

n 0.01 i 0.00

H 0.02 ∆ 0.04 0.02

5500 6000 6500 julian date - 2 450 000 0.06 0.04 0.02 0.00 0.02 0.04 0.06 0.08 1 ∆FWHM [km s− ] Fig. 4. Magnetic cycle of WASP-41. Top: FWHM of the CCF from the CORALIE measurements. Bottom:Hα index extracted from the Fig. 7. Correlation between the Hα index and the FWHM from HARPS CORALIE spectra. The red lines correspond to the ﬁtted third-order data of CoRoT-7. trend.

. . 3.3. Analysis 0.35 As we did with WASP-47, we simultaneously fitted the tran- 0.30 sit light curves and the radial velocity measurements with an 0.25 MCMC algorithm. To define the priors for the limb-darkening 0.20 coefficients of the non-standard TRAPPIST I + z filter, we took 0.15 the average of the values of the standard filters Ic and z0, and 0.10 the quadratic sums of their errors. We did not include the FTS Normalised power Normalized power 0.05 photometry from the discovery paper in our analysis because it 0.00 suffered from poor weather conditions. As suggested by Gillon 2.5.10.0 20. 50. 100.0 200. 500. 1000. et al.(2012), we included a quadratic polynomial in time to . Period [days] . model the transit light curves (except the fourth TRAPPIST and the first Danish transit observations). Fig. 5. WASP-41 Lomb-Scargle periodogram of the FWHM after subtracting the third-order trend. A clear peak is present at 1 year. The dot- The observations with TRAPPIST on 21 Mar. 2011 and ted lines correspond to a false-alarm probability of 0.1%, 1%, and 10%. 9 Mar. 2012 suffered from malfunctions of the autofocus. As a consequence, the FWHM of the images varied a lot. To correct . . for this effect, we added a third-order and a quadratic polynomial in FWHM, respectively, to model those two light curves. The 0.30 TRAPPIST observation on 19 Apr. 2013 experienced a meridian 0.25 flip that we modelled including an offset for that light curve. The 0.20 TRAPPIST light curve from the 2 Apr. 2011 and the Danish one

0.15 from the 25 Apr. 2013 obviously exhibited stellar spot crossings. We visually identified the affected parts of the light curves and 0.10 decreased their weights by increasing the corresponding errors. Normalised power Normalized power 0.05 In general, we applied a correction factor to the error bars of the 0.00 light curves to account for red noise (values listed in Table2). 2.5.10.0 20. 50. 100.0 200. 500. 1000. To improve the fit of the radial velocities and decrease the . Period [days] . effects of stellar activity, we included a quadratic polynomial in the FWHM of the radial velocities from CORALIE. Then Fig. 6. WASP-41 Lomb-Scargle periodogram of the Hα index after sub- we quadratically added a “jitter” noise of 13.2 m s−1 to the er- tracting the third-order trend. A peak is present at ∼18 days, correspond- ror bars to equal the mean error with the standard deviation of ing to the photometric rotation period. The dotted lines correspond to a the best-fit model residuals. For the HARPS data (not includ- false-alarm probability of 0.1%, 1%, and 10%. ing the RM sequence), we added a linear dependency in FWHM and a quadratic polynomial in bisector. We also added a “jitter” noise of 6.7 m s−1 to the radial velocity error bars. The baselines in FWHM and bisector were determined by comparing the BIC and the residual jitter obtained when running short chains with various models. likely due to the magnetic cycle, a signal appears at ∼23 days, We modelled the Rossiter-McLaughlin√ effect following the corresponding to the photometric rotation period of the star. This equations of Giménez(2006). We used v sin I cos β, and similar result confirms that the Hα index is a good activity indi- √ ? v sin I? sin β as jump parameters, where β is the projected an- cator for such active stars. gle between the stellar spin axis and the planet’s orbital axis, The 400-day signal detected in the radial velocities is de- and v sin I? is the projected rotational velocity. The Rossiter– tected neither in the FWHM nor in the Hα. Its origin is most McLaughlin sequence is fitted as an independent dataset to mit- likely due to the presence of a second planetary companion. igate the effect of stellar activity. We did not need to add any

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Table 3. Median and 1 σ limits of the posterior marginalised PDFs 1.00 obtained for the WASP-41 system derived from our global MCMC

FTS z0 analysis.

0.98 MCMC Jump parameters Star T [K] 5545 ± 33 TRAPPIST I +z eff 0.96 [Fe/H] 0.06 ± 0.02 Flux c1,z0 0.819 ± 0.009 c2,z0 −0.230 ± 0.006 0.94 c1,I+z 0.85 ± 0.04 Danish R c2,I+z −0.19 ± 0.04 c1,R 1.08 ± 0.01 0.92 c2,R −0.09 ± 0.01 Planet b 2 2 1 0 1 2 Planet/star area ratio (Rp/R?) [%] 1.87 ± 0.01 0 dT [h] b = ab cos ip,b/R? 0.10 ± 0.06 T14[d] 0.1099 ± 0.0002 Fig. 8. WASP-41b transit data (blue: FTS z0; green: TRAPPIST I + z; Pb [d] 3.0524040 ± 0.0000009 red: Danish R) and best fit model (black line). The TRAPPIST light T0,b – 2 450 000 [BJDTDB] 6014.9936 ± 0.0001 curve was obtained by binning the data from five transit observations, √ eb cos ωb 0.002 ± 0.048 and the Danish one from one full and one partial transit observations. √ eb sin ωb 0.059 ± 0.074 Each point corresponds to a 7.2 min bin. q K = K 1 − e2 P1/3 [m s−1 d1/3] 199.7 ± 2.3 √2,b b b b √v sin I? cos β 1.42 ± 0.10 v sin I sin β −0.78+0.38 “jitter” or dependency on other parameters to these data. Owing ? −0.28 Planet c to the low transit impact parameter btr, there was a strong degen- P [d] 421 ± 2 eracy between β and v sin I (see Triaud et al. 2011; Anderson c ? T0,c – 2 450 000 [BJDTDB] 6011 ± 3 et al. 2011). We imposed a normal prior on v sin I to avoid un- √ ? √ec cos ωc 0.53 ± 0.02 physical solutions. Indeed from an MCMC with no prior on the ec sin ωc −0.07 ± 0.06 ◦ ◦ +10.0 −1 p v sin I we obtain β = −48 ± 29 , and v sin I = 3.5 km s 2 1/3 −1 1/3 ? ? −1.0 K2,c = Kc 1 − ec Pc [m s d ] 676 ± 21 −1 with v sin I? getting higher than 100 km s , clearly inconsistent Derived parameters with the spectral analysis. The value derived for β is strongly Star dependent on the value of the prior for v sin I? u1,z0 0.282 ± 0.005 The priors used for Teff and [Fe/H] are defined with the val- u2,z0 0.256 ± 0.002 ± ues from Mortier et al.(2013). For the v sin I? we revised the u1,I+z 0.30 0.02 value derived by Doyle et al.(2014), using the stellar parame- u2,I+z 0.25 ± 0.02 ters from Mortier et al.(2013) to estimate the macroturbulence. u1,R 0.416 ± 0.006 −1 u2,R 0.252 ± 0.004 Therefore we used v sin I? = 2.66 ± 0.28 km s as a normal Density ρ? [ρ ] 1.41 ± 0.05 prior. Since we benefitted from transit observations that span Surface gravity log g [cgs] 4.53 ± 0.02 more than three years, we did not use a prior on the period and ? Mass M? [M ] 0.93 ± 0.07 time of inferior conjunction T0,b of the transiting planet. Radius R? [R ] 0.87 ± 0.03 Luminosity L? [L ] 0.64 ± 0.04 −1 Projected rotation velocity v sin I? [km s ] 2.64 ± 0.25 3.4. Results Planet b ± We present in Table3 the median and 1 σ limits of the Mass Mp,b [MJup] 0.94 0.05 Radius Rp,b [RJup] 1.18 ± 0.03 marginalised posterior distributions after running five chains of −1 RV amplitude Kb [m s ] 138 ± 2 100 000 accepted steps (considering a 20% burn-in phase). The Orbital eccentricity e <0.026 (at 2σ) ∼ ∼ b acceptance rate is 25% ( 40% for the burn-in phase). The con- Orbital semi-major axis ab [au] 0.040 ± 0.001 ◦ vergence of the chains is validated by the test of Gelman & Orbital inclination ip,b [ ] 89.4 ± 0.3 Rubin(1992) (PSFR better than 1.01), and the autocorrelations Transit impact parameter btr 0.10 ± 0.06 ◦ +14 are shorter than 2000 steps. Including the second planet in the Projected orbital obliquity β [ ] −29−10 model undoubtedly improves the fit. The rms of the CORALIE Density ρp,b [ρJ] 0.56 ± 0.03 data after the two-planet fit is ten times smaller than after a one- Surface gravity log gp,b [cgs] 3.24 ± 0.01 ∗ planet fit. The best fit solution is plotted in Fig.8 for the transit Equilibrium temperature Teq,b [K] 1244 ± 10 light curves and in Fig.9 for the radial velocities. Again, the val- Planet c Minimum mass M sin i [M ] 3.18 ± 0.20 ues provided in Table3 are not the ones used in Figs.9 and8. p,c p,c Jup RV amplitude K [m s−1] 94 ± 3 We checked that they represent a self-consistent set of parame- c Orbital eccentricity ec 0.294 ± 0.024 ters by comparing the BIC using both sets of values (best fit and ◦ Argument of periastron ωc [ ] 353 ± 6 median of the posterior distribution) and get compatible results. Orbital semi-major axis ac [au] 1.07 ± 0.03 ∗ The best-fitting model suggests a misaligned planet with a Equilibrium temperature Teq,b [K] 241 ± 2 ◦ ◦ projected orbital obliquity of β = −28 ± 13 . However, the un- ac/R? 265 ± 3 certainties are large (see Fig. 10), and the data do not allow an aligned orbit to be excluded (P(|β| < 20◦) ∼ 24%). The ro- Notes. (∗) Assuming zero albedo and efficient redistribution of energy. tation velocity expected from the photometric rotation period

A93, page 6 of 12 M. Neveu-VanMalle et al.: Hot Jupiters with relatives

200 3.7 150

] P =3.05 d

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] P =421 d 1 100 c − s 50 2.2 m

[ 0

R 50 100 1.9 0.4 0.2 0.0 0.2 0.4 -60 -40 -20 0 20 40 60 Φ β [°] Fig. 9. WASP-41 radial velocity data (blue: CORALIE, green: HARPS; Fig. 10. Posterior distribution of β and v sin I? for WASP-41 b on loga- red: HARPS RM sequence) and best fit model (black line). Top: phase- −1 rithmic scale. We impose a prior of 2.66 ± 0.28 km s on v sin I?. The folded on the period of the inner planet (outer planet subtracted). contours correspond to the 1, 2, and 3σ confidence limits for each pa- Middle: zoom on the Rossiter-McLaughlin effect. Bottom: phase-folded rameter, and include 39.3%, 86.5%, and 98.9% of the MCMC steps, on the period of the outer planet (inner planet subtracted). respectively.

of the star (∼2.44 km s−1) is compatible within the error bars −1 with the spectroscopic v sin I? (2.64 ± 0.25 km s ), suggesting Doppler surveys. A total of nine multiple planetary systems that the star is equator-on. That reinforces the possibility of an that include a hot Jupiter (with a <0.1 au) and a second planet aligned planet. with a fully probed orbit, are known (source: exoplanet.eu). Among them, four were discovered by radial velocity surveys and five by transit surveys. Those multiple systems represent 4. Discussion ∼13% of the known hot Jupiters found by radial velocities and We have shown that finding long-period planets with instru- only ∼2% of those found by transit searches. The most obvi- ments such as CORALIE is still possible around active stars. ous explanation for this difference is historical. Radial veloc- Recognising the periodic structure of activity-related signals is ity surveys started discovering hot Jupiters well before transit essential to avoiding false detections. While spots or plages in- surveys. The hot Jupiters discovered by radial velocities have duce signals at the rotation period of the star, the evolution of been followed for more than ten years, allowing the detection their coverage of the stellar surface is correlated with the mag- of very wide companions (P > 9 years). The dedicated large netic cycle of the star. Such cycles have periods of several years transit surveys (mainly HATNet and SuperWASP) started to and must be distinguished from long-period companions. Lovis efficiently discover hot Jupiters about six years ago, allowing et al.(2011) studied the e ffect of magnetic cycles on the radial only the characterisation of relatively close companions. If we velocity measurements from the HARPS planet search sample. exclusively consider companions within 2 au, the rate of hot 0 Jupiters with companions from the Doppler sample is divided They derived empirical models of correlations between RHK and radial velocities, FWHM, contrast, and bisector spans, depend- by two. ing on the effective temperature Teff and metallicity [Fe/H] of the The difference in the rates of detected additional planets in star. However, their sample only contains “quiet” stars because systems with a hot Jupiter may also be explained by the dif- they are the preferred targets for planet searches. They consider ferent observing strategies used in Doppler and transit surveys. 0 only a handful of targets with a mean log RHK > −4.7, so their The discovery of a hot Jupiter based on radial velocity data re- results cannot be applied to active stars. The CORALIE search quires a large number of observations because the observer has 0 for planets observes stars with a broader range of log RHK than no prior information on the planet. About typically ten radial ve- the HARPS one. While the emission in the Ca II (H & K) lines locity observations are carried out to confirm the existence of a is hard to extract from the CORALIE spectra, we have shown hot Jupiter previously detected by transit. In that case the ob- that the emission in the Hα, which is easy to measure, is a good server knows the period of the planet and can plan the radial ve- 0 indicator of activity for stars with log RHK > −4.7. A systematic locity observations in order to measure the radial velocity orbit study of the correlation between the Hα emission and the ra- very efficiently. This means that, on average, hot Jupiters dis- dial velocities of active stars could help to estimate the influence covered by the Doppler technique benefit from a larger num- of magnetic cycles on radial velocity measurements of active ber of radial velocity measurements than those discovered by stars. transits. Increasing the number of radial velocity measurements The transit technique has led to the discovery of more than makes the detection of longer period planetary companions 200 hot Jupiters, while only ∼30 have been discovered by easier.

A93, page 7 of 12 A&A 586, A93 (2016)

υ And HD 187123 ∼0.6% for WASP-41c (using Kane & von Braun 2008). If we as- HIP 14810 HD 217107 sume a coplanar system where the orbit of the outer planet can be HAT-P-13 WASP-41 ◦ 10.0 uniformly distributed around 5 from the orbit of the hot Jupiter, HAT-P-46 WASP-47 Kepler-424 we obtain a transit probability of ∼6% in both cases. Detecting 1 s− the transit of the outer planet would bring strong evidence that m 5.0 80 the hot Jupiter had migrated inside the disk via gap opening (Lin ] p

u et al. 1996; Marzari & Nelson 2009). However, a non-detection J

M would not be sufficient to infer a high mutual inclination between [ 1 s− M 0 m the orbits of the planets, which would be evidence of a migration 3 scenario involving dynamical interactions (Rasio & Ford 1996; Fabrycky & Tremaine 2007; Nagasawa et al. 2008; Matsumura 1.0 et al. 2010; Naoz et al. 2011). 1 s− The next predicted inferior conjunctions for WASP-47c are m 10 2 Nov. 2016 ± 30 d and 24 May 2018 ± 43 d, with an expected 0.5 transit duration of ∼18 h. A radial velocity follow-up is ongoing 0.05 0.10 0.50 1.00 5.00 in order to improve the ephemeris. The next predicted inferior a [au] conjunction for WASP-41c (02 Nov. 2016 ± 7 d) cannot be ob- Fig. 11. Known multiple planetary systems with fully probed orbits in- served by ground-based facilities because the star is close to the cluding a hot Jupiter (a < 0.1 au). Triangles: hot Jupiter found by ra- Sun. The two following ones are 12 Jan. 2018 ± 8 d and 3 Mar. dial velocity surveys. Circles: Hot Jupiters found by transit surveys. 2019 ± 10 d with an expected transit duration of ∼13 h. Diamonds: systems presented in this paper. The black dashed lines cor- Recently, Becker et al.(2015) have announced the detec- − − respond to a radial velocity semi-amplitude of 10 m s 1, 30 m s 1, and tion of two additional transiting planets around WASP-47. We −1 80 m s assuming a circular orbit around a 1 M star. Most of these checked if the nine-day planet could be detected in our set of planets were detected only by radial velocities, thus we are plotting the radial velocities. Unfortunately, the expected amplitude of the minimum mass M sin i instead of the true mass M. signal is below the sensitivity of CORALIE for such faint stars. The geometry of this system favours disc migration theories because scattering is unlikely to have kept the inner system coplanar. Sanchis-Ojeda et al.(2015) have recently announced a low In the beginning of the WASP follow-up with CORALIE, we stellar obliquity for WASP-47 that reinforces the disc-migration started a systematic search for long-period companions around hypothesis. Recent results have shown that Kozai interactions do the WASP targets with a confirmed hot Jupiter. We have fol- not affect multi-planetary systems. In this case the outer planet lowed more than 100 WASP host stars for durations of two could have “protected” the inner planets from secular interac- to eight years, including about 90 targets followed for more tions. This system brings fundamental constraints for planetary than three years. The publication of this work is in preparation formation and migration theories. (Neveu-VanMalle et al., in prep.). In this sample only two stars with a hot Jupiter have been found to host a second planet that has completed at least one orbit. We still have a lack of multiple Acknowledgements. M. Neveu-VanMalle thanks A. Doyle for her input. The systems within 2 au compared to the hot Jupiters discovered by Euler Swiss telescope is supported by the SNSF. We thank the ESO staff at La Silla for their continuous help and support, along with the many observers radial velocity surveys. on Euler and HARPS who collected the data used in that study. This work makes Detectability thresholds can contribute to explain the ob- use of observations from the LCOGT network. TRAPPIST is a project funded served discrepancy. Figure 11 shows the multiple planetary by the Belgian Fund for Scientic Research (Fonds National de la Recherche systems (with fully characterised orbits) that include a hot Scientique, F.R.S.-FNRS) under grant FRFC 2.5.594.09.F, with the participa- tion of the Swiss National Science Fundation (SNF). L. Delrez acknowledges Jupiter, distributed in a plot of semi-major axis versus mass. The support of the F.R.I.A. fund of the FNRS. M. Gillon and E. Jehin are FNRS symbols located on the left-hand side of the plot (a < 0.1 au) Research Associates. A.C.C. and C.H. acknowledge support from STFC grants are the hot Jupiters, and the symbols on the right-hand side ST/M001296/1 and ST/J001384/1 respectively. This work has made use of the (a > 0.1 au) are the long-period planets. The dotted lines were Extrasolar Planet Encyclopaedia at exoplanet.eu (Schneider et al. 2011). drawn to visualise which planets are part of the same system. We notice that except for WASP-47 c, only the long-period planets from the Doppler-survey systems have semi-amplitudes smaller References −1 than 80 m s . Indeed, Doppler surveys target small samples of Anderson, D. R., Collier Cameron, A., Gillon, M., et al. 2011, A&A, 534, A16 bright stars, while transit surveys target large samples of fainter Bakos, G. Á., Howard, A. W., Noyes, R. W., et al. 2009, ApJ, 707, 446 stars. Besides being brighter, radial velocity targets are in gen- Becker, J. C., Vanderburg, A., Adams, F. C., Rappaport, S. A., & Schwengeler, eral less active than transit targets. This means that a better H. M. 2015, ApJ, 812, L18 Butler, R. P., Marcy, G. W., Williams, E., Hauser, H., & Shirts, P. 1997, ApJ, precision can be obtained on the radial velocity measurements 474, L115 of stars from Doppler surveys. With a higher signal-to-noise Cincunegui, C., Díaz, R. F., & Mauas, P. J. D. 2007, A&A, 469, 309 ratio, detecting smaller signals is easier around brighter quiet Claret, A., & Bloemen, S. 2011, A&A, 529, A75 stars. Smaller long-period planets might exist around stars with Curiel, S., Cantó, J., Georgiev, L., Chávez, C. E., & Poveda, A. 2011, A&A, 525, A78 a known transiting hot Jupiter, but they are out of reach of cur- Doyle, A. P., Davies, G. R., Smalley, B., Chaplin, W. J., & Elsworth, Y. 2014, rent surveys. MNRAS, 444, 3592 Knowing that WASP-47b and WASP-41b are transiting, it Endl, M., Caldwell, D. A., Barclay, T., et al. 2014, ApJ, 795, 151 is natural to wonder if their outer planetary companions tran- Enoch, B., Collier Cameron, A., Parley, N. R., & Hebb, L. 2010, A&A, 516, A33 Fabrycky, D., & Tremaine, S. 2007, ApJ, 669, 1298 sit as well. If we assume that the inclination of the outer planet Feng, Y. K., Wright, J. T., Nelson, B., et al. 2015, ApJ, 800, 22 is uniformly distributed, independently of the inclination of the Gelman, A., & Rubin, D. 1992, Stat. Sci., 7, 457 hot Jupiter, the transit probability is ∼0.4% for WASP-47c and Gillon, M., Doyle, A. P., Lendl, M., et al. 2011, A&A, 533, A88

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Gillon, M., Triaud, A. H. M. J., Fortney, J. J., et al. 2012, A&A, 542, A4 Maxted, P. F. L., Anderson, D. R., Collier Cameron, A., et al. 2011, PASP, 123, Giménez, A. 2006, ApJ, 650, 408 547 Gomes da Silva, J., Santos, N. C., Boisse, I., Dumusque, X., & Lovis, C. 2014, Meunier, N., & Delfosse, X. 2009, A&A, 501, 1103 A&A, 566, A66 Mortier, A., Santos, N. C., Sousa, S. G., et al. 2013, A&A, 558, A106 Hartman, J. D., Bakos, G. Á., Torres, G., et al. 2014, AJ, 147, 128 Nagasawa, M., Ida, S., & Bessho, T. 2008, ApJ, 678, 498 Haywood, R. D., Collier Cameron, A., Queloz, D., et al. 2014, MNRAS, 443, Naoz, S., Farr, W. M., Lithwick, Y., Rasio, F. A., & Teyssandier, J. 2011, Nature, 2517 473, 187 Hellier, C., Anderson, D. R., Collier Cameron, A., et al. 2012, MNRAS, 426, Pollacco, D. L., Skillen, I., Collier Cameron, A., et al. 2006, PASP, 118, 1407 739 Queloz, D., Bouchy, F., Moutou, C., et al. 2009, A&A, 506, 303 Holman, M. J., Winn, J. N., Latham, D. W., et al. 2006, ApJ, 652, 1715 Queloz, D., Anderson, D. R., Collier Cameron, A., et al. 2010, A&A, 517, L1 Jehin, E., Gillon, M., Queloz, D., et al. 2011, The Messenger, 145, 2 Rasio, F. A., & Ford, E. B. 1996, Science, 274, 954 Kane, S. R., & von Braun, K. 2008, ApJ, 689, 492 Sanchis-Ojeda, R., Winn, J. N., Dai, F., et al. 2015, ApJ, 812, L11 Kipping, D. M. 2013, MNRAS, 435, 2152 Schneider, J., Dedieu, C., Le Sidaner, P., Savalle, R., & Zolotukhin, I. 2011, Knutson, H. A., Fulton, B. J., Montet, B. T., et al. 2014, ApJ, 785, 126 A&A, 532, A79 Lin, D. N. C., Bodenheimer, P., & Richardson, D. C. 1996, Nature, 380, 606 Southworth, J. 2011, MNRAS, 417, 2166 Lovis, C., Dumusque, X., Santos, N. C., et al. 2011, unpublished, ArXiv e-prints Triaud, A. H. M. J., Queloz, D., Hellier, C., et al. 2011, A&A, 531, A24 [arXiv:1107.5325] Winn, J. N., Fabrycky, D., Albrecht, S., & Johnson, J. A. 2010, ApJ, 718, L145 Marzari, F., & Nelson, A. F. 2009, ApJ, 705, 1575 Wright, J. T., Marcy, G. W., Fischer, D. A., et al. 2007, ApJ, 657, 533 Matsumura, S., Peale, S. J., & Rasio, F. A. 2010, ApJ, 725, 1995 Wright, J. T., Fischer, D. A., Ford, E. B., et al. 2009, ApJ, 699, L97

A93, page 9 of 12 A&A 586, A93 (2016) Appendix A: Additional plots 200 ] 150 1

− 100

s 50 0

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100

V 150 200 R 250 ]

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− 20 s 10 0 m

[ 10

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e 30 r 40 50 ]

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i 150 b 200 5500 6000 6500 7000 julian date - 2 400 000

Fig. A.1. CORALIE data of WASP-47 plotted in time. Blue/Green dots: before/after the upgrade. Top panel: radial velocities superimposed with the best ﬁt model. Second panel: residuals of the radial velocities after subtracting the hot Jupiter superimposed with the model for the second planet. Third panel: residuals of the radial velocities after subtracting the two planets. Bottom panel: bisector spans.

A93, page 10 of 12 M. Neveu-VanMalle et al.: Hot Jupiters with relatives

Fig. A.2. Radial velocity data of WASP-41 plotted in time. Blue: CORALIE; Green: HARPS; Cyan: RM sequence. Top panel: radial velocities superimposed with the best ﬁt model. Second panel: residuals of the radial velocities after subtracting the hot Jupiter superimposed with the model for the second planet. Third panel: residuals of the radial velocities after subtracting the two planets. Bottom panel: bisector spans.

−4.40

−4.45

−4.50

−4.55 Log (R’HK) −4.60

−4.65

−4.70 5650 5700 5750 5800 5850 5900 5950 6000 6050 6100 6150 JD − 2450000.0 [days]

0 Fig. A.3. WASP-41 log RHK extracted from the HARPS spectra.

A93, page 11 of 12 A&A 586, A93 (2016) Appendix B: MCMC initial values and priors

Table B.1. Initial values and priors for WASP-47.

Parameter Value Prior 1 M? [M ] 1.07 ± 0.10 ≥0 1 Teﬀ [K] 5576 ± 68 Gaussian [Fe/H] 0.36 ± 0.051 Gaussian 2 4 u1 0.4584 ± 0.0144 Gaussian, u1 + u2 < 1 2 4 u2 0.2417 ± 0.0086 Gaussian, u1, + u2 < 1 3 Pb [d] 4.1591399 ±0.0000072 Gaussian 3 T0,b – 2 450 000 [BJDTDB] 5764.34602 ± 0.00022 Gaussian 2 3 (Rp/R?) [%] 1.051 ± 0.014 uniform ≥0 3 T14[d] 0.14933 ± 0.00065 uniform ≥0 b 0.14 ± 0.113 uniform on b0 = a cos i /R , 0 ≤ b ≤ a /R tr b pq,b ? tr b ? K [m s−1] 136.0 ± 53 uniform on K = K 1 − e2 P1/3 and ≥0 b √ 2,b √b b b eb 0 uniform on eb cos ωb √and eb sin ωb,√ if > 1 then eb = 0.999 ωb 0 uniform on eb cos ωb and eb sin ωb Pc [d] 571 ± 8 uniform 0 d ≤ P ≤ 1000 yr T – 2 450 000 [BJD ] 5983 ± 26 uniform 0,c TDB p −1 ± − 2 1/3 ≥ Kc [m s ] 34 10 uniform√ on K2,c = √Kc 1 ec Pc and 0 ec 0.2 ± 0.2 uniform on ec cos ωc √and ec sin ωc,√ if > 1 then ec = 0.999 ωc 0 uniform on ec cos ωc and ec sin ωc

References. (1) From Mortier et al.(2013). (2) Interpolated from Claret & Bloemen(2011). (3) From Hellier et al.(2012). (4) See Kipping(2013).

Table B.2. Initial values and priors for WASP-41.

Parameter Value Prior 1 M? [M ] 0.90 ± 0.07 ≥0 1 Teﬀ [K] 5546 ± 33 Gaussian [Fe/H] 0.06 ± 0.021 Gaussian 2 5 u1,z0 0.2817 ± 0.0044 Gaussian, u1,z0 + u2,z0 < 1 2 5 u2,z0 0.2559 ± 0.0022 Gaussian, u1,z0 + u2,z0 < 1 2 5 u1,I+z 0.3090 ± 0.0340 Gaussian, u1,I+z + u2,I+z < 1 2 5 u2,I+z 0.2510 ± 0.0170 Gaussian, u1,I+z + u2,I+z < 1 2 5 u1,R 0.4144 ± 0.0065 Gaussian, u1,R + u2,R < 1 2 5 u2,R 0.2520 ± 0.0037 Gaussian, u1,R + u2,R < 1 −1 3 v sin I? [km s ] 2.66 ± 0.28 Gaussian 4 Pb [d] 3.052401 ± 0.000004 uniform 0 d ≤ P ≤ 1000 yr 4 T0,b – 2 450 000 [BJDTDB] 6014.991 ± 0.001 uniform 2 4 (Rp/R?) [%] 1.86 ± 0.04 uniform ≥0 4 T14[d] 0.108 ± 0.002 uniform ≥0 b 0.40 ± 0.154 uniform on b0 = a cos i /R , 0 ≤ b ≤ a /R tr b pq,b ? tr b ? K [m s−1] 135.0 ± 84 uniform on K = K 1 − e2 P1/3 and ≥0 b √ 2,b √b b b eb 0 uniform on eb cos ωb√and eb sin ωb,√ if >1 then eb = 0.999 ωb 0 uniform√ on eb cos ωb and √eb sin ωb ◦ β [ ] 0 uniform on v sin I? cos β and v sin I? sin β Pc [d] 418 ± 3 uniform 0 d ≤ P ≤ 1000 yr T – 2 450 000 [BJD ] 6006 ± 10 uniform 0,c TDB p −1 ± − 2 1/3 ≥ Kc [m s ] 94 4 uniform√ on K2,c = K√c 1 ec Pc and 0 ec 0.3 ± 0.05 uniform on ec cos ωc √and ec sin ωc,√ if >1 then ec = 0.999 ωc 0 uniform on ec cos ωc and ec sin ωc

References. (1) From Mortier et al.(2013). (2) Interpolated from Claret & Bloemen(2011). (3) Updated from Doyle et al.(2014). (4) From Maxted et al.(2011). (5) See Kipping(2013).

A93, page 12 of 12